Solve for x (x^2+x)/x=x+1

$\frac{x^{2} + x}{x} = x + 1$

Factor each term.

Factor $x$ out of $x^{2} + x$ .

Factor $x$ out of $x^{2}$ .

$\frac{x \cdot x + x}{x} = x + 1$

Raise $x$ to the power of $1$ .

$\frac{x \cdot x + x^{1}}{x} = x + 1$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot x + x \cdot 1}{x} = x + 1$

Factor $x$ out of $x \cdot x + x \cdot 1$ .

$\frac{x (x + 1)}{x} = x + 1$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{x (x + 1)}{x}$ by cancelling the common factors.

Cancel the common factor.

$\frac{x (x + 1)}{x} = x + 1$

Rewrite the expression.

$\frac{x + 1}{1} = x + 1$

Divide $x + 1$ by $1$ .

$x + 1 = x + 1$

Solve the equation.

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$x + 1 - x = 1$

Combine the opposite terms in $x + 1 - x$ .

Subtract $x$ from $x$ .

$0 + 1 = 1$

Add $0$ and $1$ .

$1 = 1$

Since $1 = 1$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$